3. Optimization of internal standard addition
3.1.5 Selection of the design
The uniform shell design of 17 experiments described in Figure 3.4 (purple trace) was the selected choice in terms of the relative low number of experiments. The matrix with 21 experiments was not considered due to the fact that the uncertainty (green trace in Figure 3.4) did not much decrease when introducing 4 more experiments (n=17+4).
Since a blank sample (wild salmon liver with an undetectable level of eicosaoinds) was not available, 3 more experimental points that involve the addition of 3 different levels of internal standard to estimate the endogenous level of eicosanoid in the liver sample were added. The extra points in questions are represented in Figure 3.5 with a red circle. The final design matrix is described in Table 3.5.
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31
Figure 3.5: Selected experimental points to estimate the response factor.
Black circles corresponds to uniform shell design experimental points, while red circles indicate samples only spiked with internal standard, also, the number in the circle indicates the number of replicates.
Experimental points marked with stars correspond to standard addition method experimental points.
Levels of PGE2 in different fish tissues (e.g. brain, kidney and heart) have been reported to be up to 50 pg/mg [90, 91]. Based on this concentration, the investigated analytical range for both PGE2 and LTB4 was set to be 1-50 ng/g.
The studied range for the PGE2-d4 and LTB4-d4 was sat to be 15-50 ng/g assuming that the level of internal standard addition should be above the lower 1/3 of the working analyte range.
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Table 3.5 the selected design matrix to estimate the response factor and the endogenous eicosanoids concentration
Experiment No.
Coded level Natural level (ng/g)
x1 x2 x1 x2
PGE2 LTB4 PGE2-d4 LTB4-d4
1 -0.0 -00.00 25.00 25.00 32.5 32.5
2 -0.5 -0.866 37.25 37.25 17.3 17.3
3 -0.5 -0.866 13.20 13.20 47.7 47.7
4 -0.5 -0.866 13.20 13.20 17.3 17.3
5 -0.5 -0.866 37.25 37.25 47.7 47.7
6 -1.0 -00.00 01.00 01.00 32.5 32.5
7 -1.0 -00.00 50.0 50.00 32.5 32.5
8 -NP -0.866 00.00 00.00 17.3 17.3
9 NP -00.00 00.00 00.00 32.5 32.5
10 NP -0.866 00.00 00.00 47.7 47.7
NP: not present
3.1.6 RF Modeling
RF behavior was studied and modeled by using Doehlert uniform shell design where the concentrations of the PGE2and LTB4with their respective deuterated internal standards were varied simultaneously (Table 3.5).
The RF was calculated by Eq. 3.1 at each of Doehlert design experimental points based on the obtained signal area of analyte and internal standard. Then the RF was explained or modeled based on the models in Eq. 3.4. The adequacy of the developed models was evaluated by the variance ratio test or Fisher ratio test (F-Test).
Optimization of internal standard addition
33
The F-test is a statistical parametric test commonly used to compare the lack-of-fit to pure error variances of a predetermined mathematical model. This statistical test is applied by calculating the variances of the lack-of-fit and pure errors by dividing their summation with respective degrees of freedom. The ratio of variance of the lack-of-fit error to that of pure error is known as experimental F-value (FCal) and used to conclude if the model fits the data by comparing with the theoretical (tabulated) F-value (Ftab). The process of an F-test can be seen in Table 3.6.
Table 3.6 The calculation of F test parameter to check the fitness of the model.
N, P, K are the number of total experiments, number of regression coefficients and number of experimental points respectively.
Parameter Equation
Variance of residual error (VRE)
Variance of pure error (VPE)
Variance of lack of fit (VLOF)
Calculated F (cal)
If FCal is less than Ftab, it means that the model explains the experimental data confidently. In some cases, it is possible to remove the non-significant regression coefficients in the Eq. 3.4 to increase the degrees of freedom and obtain a simpler model (reduced model). In this thesis, all the theoretical F-values were calculated at the 95 % confidence level of the F-distribution. Basic calculations, statistics and F-test were carried out in Excel 2010.
3.1.7 Estimation of endogeanous concentration by standard addition method.
The endogenous concentrations of PGE2 and LTB4 were estimated using the standard addition method, In this method, different amounts of standard are directly added to some aliquot of the sample and then the instrumental signal corresponding to these samples are determined. The results are plotted as shown in Figure 3.6, where the signal is plotted on the y-axis while the x-axis is graduated in terms of the concentration of analyte added. A regression line is estimated
Optimization of internal standard addition
34
and extrapolated to the point on the x-axis at which y = 0. This negative intercept on the x-axis corresponds to the amount of the analyte in the test sample [92].
In order to reduce errors related to the instrumental signal determination and systematic matrix effect, a constant amount of deuterated standard was added to each sample, and the signal of the analyte to the signal of the deuterated standard ratio SA/SISwas plotted on the y-axis. This methodology is particularly recommended in procedures for pesticide or drug residue analysis and other contaminants in food and biological matrices [93].
Figure 3.6 The estimation of the analyte concentration by the standard addition calibration.
The curve on the left is plotted by preparing six separate calibration standards, and the curve on the right is plotted by performing three measurements on the original sample and three replicate measurements on a spiked sample containing a substantial amount of added analyte.
It is worth to be mentioned that the generated regression model must be linear over the studied range of added concentration, thus, the linearity was verified using the lack of fit method mentioned previously.
The formula for the standard deviation, SxE of the extrapolated x-value (xE) is given by the equation:
(3.8)
Optimization of internal standard addition
35
Where b is the slope, n is the number of observation and
s
y/x is the residual standard deviation. Thus, increasing the number of experiments reduce the extrapolated result imprecision, also winding the range of the analyte added concentration will increase the value ∑𝑖 (𝑥𝑖 − 𝑥)2and reduce SxE.It is recommended to use six separate calibration standards (Figure 3.6, left), or perform three measurements on the original sample and three replicate measurements on a spiked sample containing a substantial amount of added analyte (Figure 3.6, right) [92]. However due to the lack of degrees of freedom, the latter approach was excluded. Moreover, due to the limitation of the salmon liver sample, it was decided to perform a total measurements of nine samples representing four experimental points (Figure 3.5).
3.2 Experimental 3.2.1 Reagents
Prostaglandin E2 (PGE2, 99%), deuterated prostaglandin E2 (PGE2-d4, 99%), leukotriene B4 (LTB4, 97%), deuterated leukotriene B4 (LTB4-d4, 99%) were purchased from Cayman Chemical (Ann Arbor, MI, USA). Acetonitrile (liquid chromatographic grade, 99.8) was obtained from Sigma-Aldrich (St. Louis,MO, USA) and Chloroform (liquid chromatographic grade, 99.8%) was bought from Merck (Germany). Liquid nitrogen and dry ice were provided by Tess (Norway).
3.2.2 Samples preparation.
The initial concentrations of PGE2, LTB4, PGE2-d4, LTB4-d4 was 50 ng/ml, two stock solutions, designated as A and B, were prepared. Solution A containing 50 ng/ml of both PGE2 and LTB4 and solution B containing 50 ng/ml of both PGE2-d4 and LTB4-d4.
A wild salmon liver sample stored at -80°C was treated according to the above described extraction procedure (sub-section 2.2.2).
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Table 3.7 Concentrations of PGE2, LTB4, PGE2-d4 and LTB4-d4 in frozen liver sample at each experimental point of a two-variable Doehlert design
Experiment No.
Coded level Natural level (ng/g) Amount
added from
Sample replication regime was corresponding to thr Figure 3.5 3.2.3 HPLC-MS/MS analysis
The LC/MS apparatus and the various instrumental and measurement conditions have been described above (section 2.2.3) however, the total analysis time was set to 20 min.
Optimization of internal standard addition
37 3.3 Results and discussion
The RF behavior for the COX metabolite (PGE2 and PGE2-d4) and the LOX metabolites (LTB4
and LTB4-d4) were modeled using a full-second order polynomial function with six coefficients (Eq. 3.4). Reduced models were also considered by ruling out less contributing coefficients.
This was done when the adequacy and prediction capacity of the reduced model was not significantly affected in comparison with the six coefficients model. The fitness of the developed models was validated by comparing the ratio of experimental lack-of-fit to pure error variance at the determined degrees of freedom Fcal with Fcrit as explained previously.
The variation of the analytes concentration between samples due to the differences in samples initial weight was considered (Appendix 1).
3.3.1 Modeling of the RF as a function of PGE2 and PGE2-d4
The signal of the blank sample was initially subtracted from the experimental signals corresponding to the spiked samples dictated by the Doehlert design to eliminate the contribution of the endogenous level.
The experimental RF values at the various levels of concentrations of PGE2 and PGE2-d4 were modeled successfully by using a six parameters regression models described by Eq. 3.4. This six parameters model was reduced to a four parameters model and expressed by:
RF = - 4.61+ 0.0306 ×[PGE2] +0.014×[PGE2-d4] - 0.009×[PGE2]×[PGE2-d4] (3.9) The statistical acceptability of Eq. 3.9 was checked by means of a F-test as shown is Table 3.8.
The RF variation as a function of PGE2 in the range of 0 - 50 ng/g and PGE2-d4 in the range of 15-50 ng/g and according to Eq. 3.9 is presented in Figure 3.7.
The contour plot (figure 3.7) revealed that the RF remains constant in the whole range of PGE2 when the internal standard is varied between (31.5 -32.5) ng/g.
Based on the RF behavior (Figure 3.7), a concentration of 31 ng/g of PGE2-d4 was selected as the optimal concentration of PGE2-d4 internal standard to analyze quantitatively PGE2 in salmon liver.
Optimization of internal standard addition
38
Figure 3.7 Contour plot of the response factor (RF) expressed as a function of PGE2-d4 vs.
PGE2
Table 3.8 Statistical validation results of the RF models for selecting optimal levels of internal standards associated with the analysis of LTB4 and PGE2 Salmon Liver.
PGE2 LTB4
Residual Variance 12.46 0.23
Pure Error Variance 16.97 0.14
Lack Of Fit Variance 3.39 0.35
F calculated 0.199 2.49
F tabulated 3.700 3.700
3.2 Modeling of the RF as a function of LTB4 and LTB4-d4
Similarly to the COX metabolite, the experimental RF values at the various levels of concentrations of LTB4 and LTB4-d4 were modeled successfully, after subtracting the blank signals, by using a six parameters model of the form:
RF = - 4.61+ 0.306× [LTB4] - 0.140× [LTB4-d4] - 0.009×[LTB4] [LTB4-d4] (3.10)
Optimization of internal standard addition
39
The statistical acceptability of Eq. 3.9 was checked by means of a F-test as shown is Table 3.8.
The model could not be reduced furtherly.
The RF contour plot generated by Eq. 3.10 as a function of LTB4 and LTB4-d4 in the range of 0 - 50 ng/g and 15-50 ng/g respectively (Figure 3.8) displays three major regions, in which RF varied along LTB4 axis, however, with the high concentration of LTB4-d4 (between 45-50 ng/g) the RF tends to be constant over the whole LTB4 studied concentration range.
Based on the RF behavior (Figure 3.8) a concentration of 47.5 ng/g of LTB4-d4 was selected as the optimal concentration level of internal standard to analyze quantitatively LTB4 in salmon liver.
Figure 3.8 Contour plot of the response factor expressed as a function of LTB4-d4 vs. LTB4.
Optimization of internal standard addition
40
3.3.3 Standard Addition Method to estimate the endogenous levels of eicosanoids
The quantification of endogenous levels of PGE2 and LTB4 were performed by the method of standard addition as follows. From the results of the previous Doelhert design (Table 3.5), calibration curves for PGE2 and LTB4 were generated and the concentration of the eicosanoids in the blank samples determined.
Each calibration curve was constructed from sets of four experimental points corresponding to three different levels of analyte (1, 25 and 50 ng/g) and one from the unspiked working samples.
Each selected point contained constant amounts of PGE2-d4 and LTB4-d4 (32.5 ng/g) which were added to each sample.
Two samples were prepared for each point except the point that correspond to 25 ng/g of added analyte (the central point of the Doelhert design) of which three samples were prepared.
The signal ratios PGE2/PGE2-d4 and LTB4/LTB4-d4 were plotted versus the concentrations of PGE2 and LTB4 respectively. Figure 3.9 shows the standards addition method regression curve for both PGE2 and LTB4.
The analyte endogenous concentration in the unspiked working samples was determined by extrapolating the calibration curve to the negative part of the concentration axis. Then, the absolute value of the x-intercept was calculated to estimate the amount of PGE2 and LTB4 in the unspiked blank salmon liver. The results in Table 3.9 showed that the endogenous levels were found 101.46 ±48.48 ng/g and 86.67±41.28 ng/g with the confidence level of 95% for both PGE2 and LTB4 respectively.
Optimization of internal standard addition
41
Figure 3.9 standards addition method regression curve for both PGE2 and LTB4 Where [A] is the analyte concentration andSA/SIS in the signal of the analyte to the signal of the internal standard ration.
Table 3.9 Quantification of PGE2 and LTB4 in working sample using the standard addition method
PGE2 LTB4
Standard addition Calibration line slop 0.017 -0.108 Standard addition Calibration line intercept 1.73 9.27
Endogenous concentration ng/g 101.46 86.67
RSD% 16.28 16.44
Figure 3.9 shows that generated the linear regression curve that correspond to LTB4 had a negative slop, this could be due to the major variation of the response factor, as shown in Figure 3.8., when using the concentration of 32.5 ng/g of internal standard.
Also, the LTB4 production might differ within the same liver, depending on which type of liver cells the samples contain the most. For instance LTB4 are produced in both hepatocyte and kupffer cells but not in the endothelial cells [5], these points might have affected the sensitivity of the test and caused a negative slop, however, suggestion regarding the method improvement and sample homogenization are given in section 4.8.
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3.3.4 Remodeling of the RF as a function of PGE2 and PGE2-d4 by considering the contribution of the endogenous levels (101 ng/g) in the blank salmon liver
By considering the endogenous level of 87 ng/g, the analytical range of 87-137 ng/g was estimated and the behaviors of the RF was studied as explained above (section 3.3.1). The results indicated that the suggested model was found as follows:
RF = -7.26 +0.074×[PGE2] +0.38×[PGE2-d4] -0.003×[PGE2]×[PGE2-d4] (3.11) The suggested model was validated by the mean of F-test as mentioned in table 3.10.
The RF behavior over the studied range is represented in the Figure 3.10, The RF tends to be constant when the level of internal standard varied between (20-31) ng/g
Figure 3.10 Contour plot of the response factor (RF) expressed as a function of PGE2-d4 vs.
PGE2 After considering the endogenous level of LTB4.
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43
3.3.5 Remodeling of the RF as a function of LTB4 and LTB4-d4 by considering the contribution of the endogenous levels (87 ng/g) in the blank salmon liver
By considering the endogenous level of 87 ng/g, the analytical range of 87-137 ng/g was estimated and the behaviors of the RF was studied as explained above (section 3.3.2). The results indicated that the suggested model was found as follows:
RF = - 6.85 + 0.1× [LTB4]- 0.04× [LTB4-d4]- 0.002×[LTB4] [LTB4-d4]+ 0.0022 [LTB4-d4]2 (3.12)
The statistical acceptability was checked by F-test. Table 3.10.
The RF was studied over the whole range using the equation 3.12, and plotted in Figure 3.11, the RF tends to be constant when the concertation of internal standard was set to be 50 ng/g.
Figure 3.11 Contour plot of the response factor expressed as a function of LTB4-d4vs. LTB4 After considering the endogenous level of LTB4
In order to assess the variability of the RF over the studied range on analyte concentration, another approach was used:
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Using both equations 3.11 and 3.12, the RF was calculated along the whole studied range of 87- 101-151 ng/g and 137 ng/g for both PGE2 and LTB4 respectively and the range of 15 – 50 ng/g regarding both PGE2-d4 and LTB4-d4. And the variability of RF PGE2 and RF LTB4, expressed as relative standard deviation (RSD) was studied (Fig.3.12).
The RSD increased in the whole range of PGE2 as the concentration of PGE2-d4 increased in the range of 15–50 ng/g. While the RSD decreased in the whole range of LTB4 as the concentration of LTB4-d4 increased in the range of 15–50 ng/g.
On average, it was estimated that the optimal concentrations of PGE2-d4 and LTB4-d4 yielding constant RF PGE2 and RF LTB4, in the whole range of PGE2 and LTB4 and with the minimum dispersion, lies between 25-30 ng/g and 45-50 ng/g respectively.
The optimal selected concentration was 25 ng/g and 50 ng/g for both of PGE2-d4 and LTB4-d4 respectively.
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Figure 3.12 Average PGE2 and LTB4 response factors (RF PGE2 and RF LTB4) and associated relative standard deviations (RSD%) at different concentration ranges of PGE2-d4 and LTB4 -d4. The green bars represent optimal concentrations of internal standards (in ng/ml) yielding constant RF and minimum RSD in the whole range of analytical concentrations.
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Table 4.1 PGE2 and LTB4 calibration curves regression coefficients and statistical validation results for the obtained model.
PGE2 LTB4
Correlation Coefficient 0.40 0.48
Variance of residual error (VRE) 0.71 0.18
Variance of pure error (VPE) 0.48 60.20
Variance of lack of fit (VLOF) 0.62 0.85
Calculated F (Fcal) 1.30 0.96
Tabulated F (F tab) 5.78 5.78
3.4 Conclusions
The two-factor Doehlert uniform shell design demonstrated to be an efficient strategy to estimate rationally and comprehensively the optimal levels of internal standards, specifically PGE2-d4 and LTB4-d4, in addition to the analytical range for PGE2 and LTB4 where is expected a linear behavior.
The optimal concentration was found 25 ng/g and 50 ng/g for both of PGE2-d4 and LTB4-d4 respectively.
Standard addition method was performed to estimate the endogenous level of eicosanoids in the working sample, the endogenous level was found 101.46 ±48.48 ng/g and 86.67±41.28 ng/g with the confidence level of 95% for both PGE2 and LTB4 respectively.
.
Method Validation
47
4. Method Validation
Method validation is the confirmation of the method precision and reliability by defining the characteristic of the method to guarantee that the procedure, when correctly applied, produces results that are fit for purpose [1, 82].
After the selection of the optimal internal standard concentrations, the developed LE-HPLC-MS/MS method was submitted to analytical validation. The considered validation parameters were: selectivity, limit of detection, limit of quantification, linearity, analytical range, precision recovery and stability.
4.1 Selectivity
Selectivity of a method is defined by the ability of the method to determine a particular analyte in a complex mixture without interference from other components in the mixture [95].
In chromatographic techniques compounds are separated and eluted in different retention times which can guarantee the selectivity, the selectivity is assessed by the terms Resolution (Rs) which is defined by the equation:
Rs =
1 Δ𝑡2 (𝑊𝐴−𝑊𝐵) (4.1)
While
Δ𝑡
is the separation time difference between two peaks and W is chromatographic peak width at base [1, 95].When the chromatographic method is coupled with mass spectroscopy, the mass spectra guarantee more selectivity [96].
In this thesis the selectivity was assessed by evaluating the extracted ion chromatogram EIC of PGE2, LTB4, LTB4 –d4 and PGE2 - d4. As shown in Figure 4.1, the method was highly selective, this selectivity allows the use of isotopically labelled analytes as internal standards, and distinguish between the obtained signals.
Method Validation
48
Figure 4.1 EIC of PGE2, LTB4, LTB4 –d4 and PGE2 -d4 spiked in a wild salmon liver sample.
4.2 Linearity
Linearity is the ability of an analytical method to provide an analytical response proportional to the concentration or the amount of analyte within a specified range of analyte concentration [83].
Linearity is expressed by the linear regression equation:
𝑦 = 𝑎 (𝑥) + 𝑏 (4.2)
Where y, in the present study, is the analyte/internal standard signal ratio, x is the analyte concentration and a and b are the slope an intercept of the calibration function respectively.
In common practice the linearity of a calibration curve is assessed by calculating the correlation coefficient (r) [95].
r =
𝑛 ∑ 𝑥𝑖𝑦𝑖−∑ 𝑥𝑖 ∑ 𝑦𝑖√[𝑛 ∑ 𝑥𝑖2−(∑ 𝑥𝑖)2][𝑛 ∑ 𝑦𝑖2−(∑ 𝑦𝑖)2]
(4.3)
A correlation coefficient close to unity (r = 1) is traditionally considered sufficient evidence to conclude that the experiment has a perfect linear calibration. However, the correlation coefficient close to one does not necessarily imply the linearity of a regression model.
Moreover, the linearity must be checked using the F-test previously described in the section 3.1.6.
Method Validation
49
The developed method was assessed by using Eq. 4.2 in the range of 1-50 ng/g of PGE2 and
The developed method was assessed by using Eq. 4.2 in the range of 1-50 ng/g of PGE2 and